Actually I have a problem with this quest. I can't complete it. I'm in the chapter 6 on the serawi route, first game, and Ragsmuena just joined me as a guest.
At first I left this quest for some later time, since it was "improve your alchemist skills". However in the middle of 6th chpater, I saw on the wiki that this quest can be completed at at chapter 5. But I didn't get any recipes for it or for materials, or anything ;/
What is more, I couldn't find any info how exacly complete this quest (searched this forum, as well as google).
I try do do as many quest and events as possible, also try to clear areas at 100%, so I though increasing my rank will advance this quest..
Am I missing something important?

You can't fail that quest, no need to worry.

I completed it on Yuela's route CH 4, NG. Not sure if you can fix it on other routes.
The requirements also include "research flame elementals" (Uya) and "research flame elementals" (Melodiana)

did u buy the northen book from the merch this help a lot .... if u r in not yuela route then u finish that quest around chapter 6ish if u r in her route chapter 4 is the time u finsih that quest to get her h scene

Thanks for replies!
I advanced to chapter 7, and at the beginning I got a scene wit fixing her sword.

I just got a little scared, thinkng I missed something big since:
1) It's the first quest
2) seemed pretty imporant to the plot

But it was kinda disappointing, nothing happened and I have much better swords for her.. Well, maybe on her route (I'm on Serawi) it will be different (no spoilers plz ).

Well, it can be leveled for a few more stat points (not much iirc, 3 more strength in total.) and can be further upgraded in chapter 9 if you max it out and have 200 sense/knowledge. It then gets the omni element as opposed to Holy which can be good/bad depending on if you have a secondary Holy weapon.

Mind, in that same chapter you can complete Yuela's arena challenge and get a very powerful Holy weapon so either way, it's usage is pretty limited. I forgot that you can also forge Reyshia swords once you gain access to Reyshia shells and it's equally powerful as an Omni weapon unless you're fighting a specific type of enemy.

NG+, it finally becomes really powerful as you can upgrade it once you get the first NG+ item, maxing that item allows you to craft another ultimate sword.

I find that near the end of the game, the bulk of your power will come from base stats anyway, the main reason you'd use different weapons is for the elements they give.

Edit: Whoops, you can only upgrade it once more in NG+, Kitchen Knife isn't an upgrade of that item despite needing it to be maxed to unlock the recipe.

remember to keep all ur weapon for the elem bonus and do the extra story ( complete the bonus too to get cg) .... and u get three extra character ....

It's a good sword for Yuela's route on NG for a while since you get it earlier. =P

CH 4, it's closest competitor was Mithril sword at 5 STR and 5 EVD lower.
With 3 Hits, it's a loss of 15 damage and the small free regen (better than nothing at that time).
You'll rather use the Holy-based sword against undead than Mithril sword too.
CH 5, it was the Ninja Blade, which had a different function so difficult to compare.